Welcome to the website of the APDE group in Bilbao (at BCAM and EHU) working in mathematical analysis, partial differential equations, inverse problems, mathematical physics, and related topics.
BCAM, November 5th, 2026, 17:00 - 18:00
Counterexamples for generalizations of the Schrödinger maximal operator
Rena Chu - University of Göttingen
In 1980, Carleson asked for the minimal “smoothness” $s$ required of an initial data function to guarantee pointwise convergence for the solution of the linear Schrödinger equation. After progress by many authors over many decades, this was resolved by Bourgain, whose counterexample construction proved a necessary condition of $s\geq n/(2(n+1))$, and Du and Zhang, who proved a sufficient condition of $s> n/(2(n+1))$. In contrast, Rogers, Vargas, and Vega studied the analogous question for the non-elliptic Schrödinger equation and proved that, for all $n\geq 2$, $s\geq 1/2$ is necessary and $s>1/2$ is sufficient. In this talk, we consider generalizations of Carleson's question and give an overview of recent methods and results.
Current organizers: Daniel Eceizabarrena (BCAM), Mikel Florez (EHU), Arnab Roy (BCAM).